Let X be a n×p real matrix with coherence μ(X)=maxj≠j′|XjtXj′|. We present a simplified and improved study of the quasi-isometry property for most submatrices of X obtained by uniform column sampling. Our results depend on μ(X), the operator norm ‖X‖ and the dimensions with explicit...

As is well known, the likelihood in the Gaussian mixture is unbounded for any parameters such that a Dirac is placed at any observed sample point. The behavior of the EM algorithm near a degenerated solution is studied. It is established that there exists a domain of attraction around degeneracy...